Gravity surveying is one technique in modern exploration for mineral and petroleum commodities. For example, detection of geophysically significant subsurface anomalies potentially associated with ore bodies or hydrocarbon deposits can be made using gravity surveying techniques since the existence of gravitational anomalies usually depends upon the presence of an excess or deficit mass associated with the deposit. At any observation point within an arbitrary volume unit, the gravity field at that observation point can be resolved into x, y, z components with respective magnitudes that are a function of the location of that observation point relative to any mass inhomogenieties. And, the gravitational field can be directly related to geological structures and anomalous densities such as salt, or massive sulfides, for example. When used in conjunction with other geological data, gravity survey data helps to confirm the true geometry of a geological shape before drilling, for example.
As one example, the gravitational anomaly of a body of ore with a density contrast of 300 kg m−3 and a dimension of 200 m buried at a depth of 100 m is typically 20×10−6 ms−2, for example, which is about 0.00002% of the normal Earth gravity field. This relatively small effect is normally measured in units of milli gals (mGal), which is the unit for the free air and Bouguer gravity field measurements and is equivalent to 10−5 m/s2. Thus, for the above example, the body of ore would be represented by about 2 mGal.
Some geophysical prospecting has progressed towards gravity gradiometry. In principle, measurement of a gradient of a gravity field over a known baseline allows accelerations due to motion of the platform itself to be cancelled out. Gravity gradients are the spatial derivative of the gravity vector field (e.g., a second order derivative of the gravitational potential), and have units of mGal per unit distance such as mGal/km. The standard unit of gravity gradiometry is the Eötvös (E), which is equal to 10−9 s−2 or a tenth of a mGal over a kilometer (e.g., gradient signatures of shallow Texas salt domes are typically 50-100 E).
Gravity-Gradient Instruments (GGI) are used to measure the gravity gradients over an area. However, vibrations of a vessel carrying the GGI or other forces may cause the GGI to rotate a few milli-radians about the x or y body axes of the GGI. GGI measurements can be affected by such rotations. For example, such rotations cause accelerometers within the GGI to sense a centripetal acceleration. The centripetal acceleration results in a measured centripetal gradient that cannot be distinguished within the measured gravity gradients. For example, a rotation rate of 3.1×10−4 radians per second will generate an apparent gravity gradient of approximately 1E. Further, because the magnitude of the centripetal acceleration is related to the tangential speed and angular velocity as follows:
                              A          c                =                                            v              t              2                        r                    =                      r            ×                          ω              2                                                          Equation        ⁢                                  ⁢                  (          1          )                    where r is the radius of the rotations and ω is the angular rate of the rotations, then the gradient (e.g., the first derivative with respect to r) is ω2, and this squared product may translate effects from higher frequency angular rotation rates into low frequency noise. Measured signals may then be distorted if the low frequency noise is in the same frequency range as the measured signal, for example.
As a solution, GGIs are usually angularly decoupled from the vessel (e.g., marine or aircraft vessel) that carries the GGI. Decoupling can be accomplished by mounting the GGI on a gyro-stabilized table. Unfortunately, however, such stabilized tables may only be able to isolate the GGI from rotational rates up to a certain frequency (e.g., up to 20 Hz) due to the mass of the table, which in turn, is driven by the size and weight of the GGI, the compliance between the stable table and the gyroscopes, and the gain versus frequency of applied torque, for example. Thus, higher frequencies of vessel motion, such as mechanical and acoustical noise including engine and propeller noises may not be eliminated, and may be included in measurements by the GGI.
GGI measurements can also be affected by misalignment errors within the mechanics of the instruments. For example, GGIs include mechanical assemblies either directly or as part of the instrumentation system. Because the GGIs are not perfect, the GGIs can include mechanical alignment errors that can cause errors in measurements. The alignment errors can vary over time, environmental conditions and environment history, for example, such as power shut down resulting in large temperature changes, shock due to equipment handling and hard landings, and pressure and humidity changes.
Further, GGIs contain mechanical or electro/mechanical devices to measure the changes in local gravity forces. Such devices may include an accelerometer that has a proof mass, which is restrained by either electrical or mechanical means. The electrical or mechanical restraining force, when properly scaled, is a direct measure of the sum of both acceleration and gravity forces. Because the proof mass cannot be completely restrained to zero motion in any and all directions at all times, non-linearities can occur in output measurements. These non-linearities include the squared, cubic and higher order terms of the applied force and the cross product terms of the orthogonal forces, e.g., F(K1x+K2x2+K3x3+K4xy+K5xz+K6yz+K7zz+K8yy). In this example, F is the applied gravity and acceleration force in each direction, and K1 represents the scaling of the linear term and thus scales the desired output. K2 through K8 are typically 1/10^6 to 1/10^7 as compared to K1. However, since measured differences in gravity force on the order of 1/10^11 are desired, such nonlinearities become significant.